1 Introduction; 2 Defining the Sciences; Aristotle's Accounts; Ptolemy's Definitions Are Not Aristotle's; Ptolemy's Aristotelian Definitions; Conclusion; 3 Knowledge or Conjecture; Ptolemy's Epistemology: Neither Aristotle's nor Plato's; Platonic Epistemology; Ptolemy on Opinion and Knowledge; The Indisputability of Mathematical Demonstration; Mathematics' Contribution to Physics and Theology; Conclusion; 4 Mathematics and the Good Life; The Distinction between Theoretical and Practical Philosophy; Virtues

How to Order ActionsResembling the Divine; Conclusion; 5 Harmonia; Harmonia: What and Where It Is; The Beauty of Mathematical Objects; Harmonics; Harmonic Ratios in the Human Soul; Harmonic Ratios in the Heavens; Conclusion; 6 Harmonics and Astronomy; Cousin Sciences; Sure and Incontrovertible Knowledge?; Different Methods, Different Claims to Truth; Consequences; 7 Mathematizing the Human Soul; The Nature and Structure of the Soul in On the Kritêrion and Hêgemonikon; The Structure of the Soul in the Harmonics: The Aristotelian Account; The Development of Ptolemy's Scientific Method

The Structure of the Soul in the Harmonics: The Platonic and Synthetic AccountsConclusion; 8 Astrology and Cosmology; Astrological Conjecture; Celestial Powers and Rays; Celestial Souls and Bodies; Conclusion; 9 Conclusion; Bibliography; Index.